Stats Lecture 5 Fall
NonParametric Data
“ Parametric Tests” – look at one parameter and how its correlated to other variables
 Estimation of population parameters from sample parameters
 Must satisfy several assumptions: independence, normality, homogeneity
Independence
 Participants are randomly assigned to treatment conditions
 Only one observation per participant
Normality
 Data (scores) are distributed normally
 Not skewed or bimodal
 Can fix and make a curve normal or put it into another distribution..
 Cannot use parametric tests anymore once perfect normality is violated
Homogeneity
 Variances across groups and/or treatment conditions are “reasonably” similar
 Often a problem in Special Populations research where one group (and the scores they
generate) may be fundamentally different from another group
Analysis of NonParametric Data
“Parametric”
 Normal distribution
 Interval or ratio data
 Often data do not fit these criteria… nominal, ordinal (ranked)
 Exercise physiology questionnaire data, rank orderings, interrater reliabilities, etc
 Hypothesis testing and associative analyses can be used on these data; most common are:
o Chi square, spearman rank order correlation, mannwhitney U test, kruskalwallace
ANOVA by Ranks
2
Chi Square (x )
 Compares two or more sets of Nominal data that have been arranged by frequency counts
 There is no variability within a category
o Categories are mutually exclusive
o All observations are of equal value  Provides information as to whether a relationship between two independent variables occur by
chance alone
 Computed from tables of frequencies
o Comparison of counts
o Assesses discrepancies between:
Expected frequency (chance)
Observed frequency
 Letter grades are a good example; there will be a frequency distribution of A, B, C, D,… etc.
o These are nominal data IF all we are concerned with is the frequency of occurance
o A=B=C=D
2
o X analysis will determine If the frequencies within each category differ by amounts
larger than chance
 H 0ssumes any differences occurred by chance
 If H0is not true, some other factor must be involved to influence the changes in the frequency
count
 Chance principle: “is what has been observed the same or different from what is expected?”

 Sum of the squared differences between observed and expected scoeres after dividing b the
expected frequency
 Example:
 Does gender influence adherence to a cardiac rehab program?
 IV1 = Gender (make, female) , 1V2 = adherence (stayed in, dropped out)
 Computing a 2x2 Chi square:
 This is called a Tabular analysis (aka crossbreaks) .. usually these tables are bivariate
 Summarizes the “intersection” of IVs and DVs
IV(1)
1 2
IV(2) 1 DV DV
2 DV DV
 Tabl
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